The semiconductor industry is at a crisis because much finer resolution is required to meet their needs as they progress to the 10-nm, 7-nm, and finer lithography nodes to meet the demand for improved device performance. For example, while the chip capacity in flash memory increased by 100-fold from 2005 to 2013 the number of reliable state changes decreased at each step to finer lithography so the reliable capacity has actually stagnated [A. A. Chien and V. Karamcheti, “Moore's law: the first ending and a new beginning,” IEEE Computer 46 (2013) 48-53].
Roadmaps for the semiconductor industry have required that the spatial resolution in dopant and carrier profiling be finer than 10 percent of the dimension at each lithography node. While atomic resolution has been achieved in dopant profiling with the destructive process of atom probe tomography [K. Inoue, F. Yano, A. Nishida, H. Takamizawa, T. Tsunomura, Y. Nagai and M. Hasegawa, “Dopant distributions in n-MOSFET structure observed by atom probe tomography,” Ultramicroscopy 109 (2009) 1479-1484], this provides verification of the device fabrication but carrier profiling is essential to validate how a device will operate. Round-robin testing and status reviews have led the semiconductor industry to select scanning spreading resistance microscopy (SSRM) and scanning capacitance microscopy (SCM) as their primary methods for carrier profiling. SSRM is generally chosen below the 40 nm lithography node where finer resolution is required as it is claimed to provide a sub-nanometer resolution [T. Hantschel, M. Tsigkourakos, L. Zha, T. Nuytten, K. Paredis, B. Majeed, and W. Vandervorst, “Diamond scanning probes with sub-nanometer resolution for advanced nanoelectronics device characterization,” Microelectronic Engineering 159 (2016) 46-50] and SCM is generally not used at these finer nodes. However, the actual resolution for this destructive process is approximately 50 nm—comparable with the diameter of the tip-sample contact. At the 7-nm node, which was introduced by IBM in 2015, the resolution obtained with SSRM is approximately seven times the dimension of the node. Thus, at the present time, this deficiency may be likened to trying to manufacture an automobile using a string seven times the length of the car for all measurements.
In SSRM a probe, typically made of diamond which is doped to be electrically conductive, is inserted into the semiconductor and the resistance between this impact point and a much larger contact to the semiconductor is measured. Generally, most of this resistance occurs near the contact, termed “spreading resistance,” which is given by RS≈ρ/4a for an ohmic conductor, where ρ is the resistivity and a is the radius of the contact. The carrier density may be calculated from the measured resistance. However, the contact between the probe and a semiconductor is not ohmic so it is necessary to use at least one calibration curve made using the same instrument with standardized semiconductors to determine the resistivity of the semiconductor from the measured resistance. The use of calibration curves is made necessary as the physics of the nonohmic interaction have yet to be quantified. As such, any calibration must be made with known measurements of samples of the same material, type of dopant and using the same bias polarity and the same probe.
The contact between the probe and sample is also necessarily destructive of the sample, and often of the probe. The resolution for SSRM is thought to be as fine as 2.5 nm [K. Arstila, T. Hantschel, C. Demeulemeester, A. Moussa and W. Vandervorst, “Microfabricated diamond tip for nanoprobing,” Microelectron. Eng. 86 (2009) 1222-1225] or even 1 nm or finer [L. Zhang, H. Tanimoto, K. Adachi and A. Nishiyama, “1-nm spatial resolution in carrier profiling of ultrashallow junctions by scanning spreading resistance microscopy,” IEEE Electron Dev. Lett. 29 (2008) 799-801]. However, these dimensions are much smaller than the extent of the lattice distortion that is caused by the nanoindentation of the probes which is required [K. Mylvaganam, L. C. Zhang, P. Eyben, J. Mody and W. Vandervorst, “Evolution of metastable phases in silicon during nanoindentation: mechanism analysis and experimental verification,” Nanotechnology 20 (2009) 305705] so it is possible that the results may not be an accurate characterization of the semiconductor.
FIG. 1 shows an SSRM line scan made with a calibration structure that has a number of layers of silicon having different dopant densities [T. Hantschel, et al., Microelectronic Engineering 159, supra]. No error bars are given in FIG. 1 because the destruction of the sample makes it impossible to repeat a line scan. Also, if the resolution were actually 1 nm, one would expect to see a staircase having sharp 90° angles at the corners. However, in this paper which claims to show sub-nanometer resolution, there is a curving at each corner that corresponds to an actual resolution of approximately 50 nm which is the approximate diameter of the tip-sample contact. In theory, deconvolution could be used to remove the roundedness at the corners of the plot in FIG. 1. However, this is not possible with SSRM because the destructive process changes the properties of the sample up to each new point in the line scan. Non-destructive measurements, which are not possible with SSRM, may provide quasi-continuous line scans. Also, deconvolution, when an impulse function is known, can be used to improve resolution when a non-destructive measurement process is used.
Therefore, new technology for carrier profiling is required as the semiconductor industry progresses to finer lithography nodes for progress to new devices having improved performance in accordance with Moore's law. The first commercial products containing devices at the 22 and 14 nm nodes were introduced in 2012 and 2014, respectively. On Jul. 9, 2015, an alliance led by IBM Research announced production of the first 7 nm node test chips with functioning transistors. This step was made ahead of schedule because it had not been expected to occur until 2018-2019. Thus, the rule-of-thumb in roadmaps for the semiconductor industry, that the resolution for carrier profiling should be finer than 10% of the lithography node, requires sub-nanometer resolution at the 7 nm node, and for smaller nodes for which research is already in progress. To summarize, accurate carrier profiling with a resolution of 0.7 nm is now required at the 7 nm node and a resolution of 0.5 nm and 0.2 nm will be required at the 5 nm and 2 nm lithography nodes. Limitations of scanning spreading resistance microscopy:
It is hypothesized that SSRM measurements may actually have several different mechanisms. For example, in carrier profiling by SSRM the ideal relation for spreading resistance, R=ρ/4a (where p is the resistivity and a is the radius of a circular contact), is replaced by the nonlinear relation R=f(ρ) requiring calibration with standard samples [P. Eyben, M. Xu, N. Duhayon, T. Clarysse, S. Callewaert and W. Vandervorst, “Scanning spreading resistance microscopy and spectroscopy for routine and quantitative two-dimensional carrier profiling,” J. Vac. Sci. Technol. B 20 (2002) 471-478]. Examples of calibration curves, log-log plots of the measured resistance vs. the known resistivity of the standards, are irregular, frequently non-monotonic, and often non-linear with a mean slope as low as 0.6 where 1 would be expected. Furthermore, the measurements are also sensitive to surface states in the semiconductor [P Eyben, S. Denis, T. Clarysse and W. Vandervorst, “Progress towards a physical contact model for scanning spreading resistance microscopy,” Mat. Sci. Engineering B 102 (2003) 132-137], and p-type samples and n-type samples of the same semiconductor have distinctly different calibration curves [T. Delaroque, B. Domenges, A. Colder and K. Danilo, “Comprehensive nanostructural study of SSRM nanocontact on silicon,” Microelectronics Reliability,” 51 (2011) 1693-1696]. This journal article being incorporated by reference herein in its entirety.
Testing the Validity of the Concepts Behind SSRM
For an ideal small circular contact at the surface of a semiconductor the spreading resistance is given by RS=ρ/4a, where ρ is the resistivity and a is the radius of the contact. Thus, if the concept of spreading resistance were appropriate in Scanning Spreading Resistance Microscopy (SSRM) one would expect that ρ/4RS would be equal to the effective radius of the contact, a. In SSRM, the measured resistance, which is thought to be primarily spreading resistance, is measured in several standard samples of the same semiconductor having different known values of resistivity, and the measured values of RS are plotted as a function of the resistivity. Then carrier profiling is accomplished by measuring the local spreading resistance at various locations on the test sample and using the calibration data to determine the corresponding values for the local resistivity.
If the conceptual basis of SSRM were valid one would expect that the effective radius of the contact should be independent of the resistivity. FIG. 2 shows the apparent variation of the effective radius as calculated from the calibration data in [T. Hantschel, M. Tsigkourakos, J. Kluge, T. Werner, L. Zha, K. Paredis, P. Eyben, T. Nuytten, Z. Xu and W. Vandervorst, “Overcoated diamond tips for nanometer-scale semiconductor device characterization,” Microelectronic Engineering 141 (2015) 1-5], this journal article being incorporated by reference herein in its entirety. Note that there is more than a factor of 5 variation in the effective radius. Most notably, the Full Diamond Tips (FDT) have an effective radius of atomic size (0.1 nm) in one region—which is not reasonable—and ten times this at another point. Furthermore, Overcoated Diamond Tips (OCD), which were reported to provide nanometer resolution, and are described as the best [T. Hantschel, et al., Microelectronic Engineering 141, supra], have an effective radius that is much greater than that for the other two types of tips and exceeds 7 nm at one point.
FIG. 3 shows the apparent variation of the effective radius of the contact as calculated from the calibration data for p-type silicon in Delroque, et al. These data were taken when four different pressures were applied to insert the probes into the standard samples at different unknown depths. Note that the effective radius is increased at greater pressures as would be expected. However, there is about a factor of 3 variation in the effective radius at each pressure, and the dependence of the effective radius on the resistivity is not monotonic and differs appreciably from that shown in FIG. 2.
In conclusion, the method of SSRM can only be used to determine the resistivity of a semiconductor by:                (1) Measuring the resistance of the new semiconductor sample.        (2) Preparing a table with the resistance and resistivity for a group of standard samples prepared using the same semiconductor with different doping densities of the same dopant.        (3) Interpolating the table to determine the resistivity which corresponds to the resistance measured for the new sample.Previous Uses of a Microwave Frequency Comb        
The previous art pertaining to the use of a Microwave Frequency Comb (MFC) for characterizing semiconductors relates to two different methods, SCM and SSRM, which were previously used without the MFC and thus they have different inherent limits for their resolution.
(1) Depletion Capacitance—
U.S. Pat. No. 5,065,103 describes how to make electrical measurements of the depletion capacitance in order to determine the carrier concentration (though they claim dopant concentration) prior to the discovery of the MFC. More recently U.S. Pat. No. 8,601,607 describes how to measure the attenuation of the MFC with a reverse biased semiconductor. Thus a depletion layer is formed in the semiconductor and the effect of the depletion capacitance on the attenuation of the MFC is used to determine the carrier concentration (though it also claims dopant concentration). The resolution using this method would be limited by the fringing capacitance between the base of the depletion layer and the shank and connections to the tip as it is in SCM.
(2) Spreading Resistance—
U.S. Pat. No. 5,585,734 describes how to measure the spreading resistance to determine the carrier concentration prior to the discovery of the MFC. U.S. Pat. No. 9,442,078 describes how to measure the attenuation of the MFC, which is caused by the spreading resistance in order to determine the carrier concentration. All four of these patents being incorporated by reference herein in their entirety.